"When Andrew Wiles of Princeton University proved Fermat's last theorem several years ago, he took advantage of recently discovered links between Pierre de Fermat's centuries-old conjecture concerning whole numbers and the theory of so-called elliptic curves. Establishing the validity of Fermat's last theorem involved proving parts of the Taniyama-Shimura conjecture. Four mathematicians [Conrad, Taylor, Breuil, Diamond] have now extended this aspect of Wiles' work, offering a proof of the Taniyama-Shimura conjecture for all elliptic curves rather than just a particular subset of such curves...."